Giải bài tập 5 trang 90 SGK Toán 12 tập 2 - Kết nối tri thức

Cho hàm số \(f\left( x \right) = {x^2} + 3\). Khẳng định nào dưới đây là đúng? A. \(\int {f\left( x \right)dx} = 2x + C\). B. \(\int {f\left( x \right)dx} = {x^2} + 3x + C\). C. \(\int {f\left( x \right)dx} = {x^3} + 3x + C\). D. \(\int {f\left( x \right)dx} = \frac{{{x^3}}}{3} + 3x + C\).

♚Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa

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Đề bài

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về tính chất cơ bản của nguyên hàm để tính: \(\int {kf\left( x \right)dx} = k\int {f\left( x \right)dx} \) Sử dụng kiến thức về nguyên hàm một tổng để tính: \(\int {\left[ {f\left( x \right) - g\left( x \right)} \right]} \,dx = \int {f\left( x \right)dx - \int {g\left( x \right)dx} } \) Sử dụng kiến thức về nguyên hàm của hàm số lũy thừa để tính: \(\int {{x^\alpha }dx} = \frac{{{x^{\alpha + 1}}}}{{\alpha + 1}} + C\left( {\alpha \ne - 1} \right)\)

Lời giải chi tiết

\(\int {f\left( x \right)dx} = \int {\left( {{x^2} + 3} \right)dx} = \frac{{{x^3}}}{3} + 3x + C\) Chọn D

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🌄 Giải bài tập 6 trang 90 SGK Toán 12 tập 2 - Kết nối tri thức Cho hàm số f(x) thỏa mãn: \(f\left( 0 \right) = 1\) và \(f'\left( x \right) = 2\sin x + 1\). Khi đó \(\int\limits_0^{\frac{\pi }{2}} {f\left( x \right)dx} \) bằng A. \(\frac{{{\pi ^2} + 12\pi - 16}}{8}\). B. \(\frac{{{\pi ^2} - 4\pi + 16}}{8}\). C. \(\frac{{{\pi ^2} + 6\pi - 8}}{4}\). D. \(\frac{{{\pi ^2} - 2\pi + 8}}{4}\).
🐻 Giải bài tập 7 trang 90 SGK Toán 12 tập 2 - Kết nối tri thức Cho hàm số f(x) liên tục trên \(\mathbb{R}\). Gọi S là diện tích hình phẳng giới hạn bởi các đường \(y = f\left( x \right),y = 0,x = - 1\) và \(x = 4\) như hình bên. Khẳng định nào dưới đây là đúng? A. \(S = \int\limits_{ - 1}^1 {f\left( x \right)dx} + \int\limits_1^4 {f\left( x \right)dx} \). B. \(S = \int\limits_{ - 1}^1 {f\left( x \right)dx} - \int\limits_1^4 {f\left( x \right)dx} \). C. \(S = - \int\limits_{ - 1}^1 {f\left( x \right)dx} + \int\limits_1^4 {f\left( x \right)dx} \).
🌺 Giải bài tập 8 trang 90 SGK Toán 12 tập 2 - Kết nối tri thức Gọi (H) là hình phẳng giới hạn bởi các đường \(y = 2\sqrt x ,y = 0,x = 0\) và \(x = 4\). Thể tích V của khối tròn xoay sinh ra khi quay hình phẳng (H) quanh trục Ox là A. \(V = 32\). B. \(V = 32\pi \). C. \(V = \frac{{32}}{3}\). D. \(V = \frac{{32\pi }}{3}\).
ﷺ Giải bài tập 9 trang 91 SGK Toán 12 tập 2 - Kết nối tri thức Cho tứ diện ABCD, gọi G là trọng tâm của tam giác BCD và M là trung điểm của đoạn thẳng AG. Khi đó \(\overrightarrow {MA} + \overrightarrow {MB} + \overrightarrow {MC} + \overrightarrow {MD} \) bằng A. \(\overrightarrow {MG} \). B. \(2\overrightarrow {MG} \). C. \(3\overrightarrow {MG} \). D. \(4\overrightarrow {MG} \).
🃏 Giải bài tập 10 trang 91 SGK Toán 12 tập 2 - Kết nối tri thức Cho hình hộp ABCD.A’B’C’D’ có tâm O và gọi G là trọng tâm của tam giác BDA’. Tỉ số \(\frac{{AG}}{{AO}}\) bằng A. \(\frac{1}{3}\). B. \(\frac{1}{2}\). C. \(\frac{2}{3}\). D. \(\frac{3}{4}\).

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